An emergency fund is a fund used for . . . emergencies.
The water heater goes out.
The transmission on the car dies.
Your right rear tire goes flat.
And the list goes on.
Emergencies are something that, if you didn't have the money saved up, you'd probably borrow it or put it on a credit card. Not good! The last thing you want to do in an emergency is get yourself into more debt.
Where do you put it? In a savings account that is easily accessible but not too accessible. You don't want it in CDs where there is a penalty for taking it out, and you sure don't want it in the stock market. I probably wouldn't keep it under your mattress either.
You can also put it in a money market account with check-writing capabilities.
Keep in mind, this is for emergencies. Not movie-night money.